If \(n(A)=35\) and \(n(A\cap B)=12\), how many elements are only in \(A\)?
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Answer and explanation
Correct answer: 23
The set A is divided into two disjoint parts: elements only in A and elements shared by A and B. Thus, \(n(A)=n(A-B)+n(A\cap B)\). Rearranging gives \(n(A-B)=35-12=23\). Therefore, option B is correct. The value 12 represents the common region, while 35 represents all of A, including that common region.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
The set A is divided into two disjoint parts: elements only in A and elements shared by A and B. Thus, \(n(A)=n(A-B)+n(A\cap B)\). Rearranging gives \(n(A-B)=35-12=23\). Therefore, option B is correct. The value 12 represents the common region, while 35 represents all of A, including that common region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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